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(Solved): Consider the function f(x)=12x5+30x4160x3+3 f(x) has inflection points at (reading from left to ...



Consider the function \( f(x)=12 x^{5}+30 x^{4}-160 x^{3}+3 \) \( f(x) \) has inflection points at (reading from left to righ
Consider the function has inflection points at (reading from left to right) , and where is and is and is For each of the following intervals, tell whether is concave up or concave down.


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Solution
The inflection point is found by using   
Find the second derivative.


Set the second derivative equal to then solve the equation .


Find the points where the second derivative is .


Split into intervals around the points that could potentially be inflection points.

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